Browsing by Author "Schweickhardt, Tobias"

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Open Access
Nonlinearity assessment and linear control of nonlinear systems
(2006) Schweickhardt, Tobias; Allgöwer, Frank (Prof. Dr.-Ing.)
Linear control may be favorable over nonlinear control because linear design techniques greatly facilitate the controller design process and because linear controllers impose lower requirements on the implementation of the control law as compared to nonlinear controllers. It is therefore a tempting idea to use linear models and linear controller design methods also for nonlinear systems. However, the assumption of linear dynamics generally implies a modelling error that has to be taken into account in the controller design process. In this work, a methodology is presented that allows to quantify the degree of nonlinearity of a system’s dynamic behaviour, to derive an optimal linear model, and that allows using this or any other linear model to design a linear controller for the nonlinear system that guarantees stability also for the nonlinear closed loop. A key component of the underlying concept is to consider the nonlinear behaviour only on a designated operating regime. This way, only nonlinear behaviour is taken into account, that also matters for the practical operation of the nonlinear plant. The presented methodology uses an input-output approach, and the operating regime is characterized by the set of admissible input signals. For special system classes, the nonlinearity measure and best linear model can be determined with given formulas, while optimization techniques are used for general system classes. The results for controller design are built on concepts from robust control. The nonlinear plant it therefore devided into a nominal linear model and a nonlinear error term. The given stability conditions then allow to design a linear controller for the saturated nominal linear model such that the closed loop remains stable if the nonlinear error term is present.